The module comprises eight units:
Unit 1: The nature of algebra
You’ll meet some definitions of school algebra and algebraic thinking. You’ll tackle problems that approach algebra as a way of exploring and expressing generality. And read about moving between well-chosen examples and generalisations, and appreciating the role of freedoms and constraints. Additionally, you’ll develop algebraic expressions for simple numerical problems and encounter ideas from research and classroom practice about learning to interpret and treat algebraic symbols.
Unit 2: Representing structural relationships
You’ll tackle problems involving making algebraic conjectures and convincing yourself when these are true. Taking an approach that algebra is a way of noticing underlying structure, you’ll meet a range of early-algebraic representations used in classrooms, such as bar models and Cuisenaire rods. You’ll read about choosing algebraic representations and work on problems with a learner.
Unit 3: The power of symbolising
This unit focuses on the power of using algebra symbols and the difficulties people experience. You’ll reflect on our choices when symbolising and how symbols help create convincing proofs. Additionally, you’ll meet the module idea ‘Manipulate, Get a sense of, Articulate’ that connects learning progression with choice of representations.
Unit 4: Equivalence and the equals sign
You’ll read and tackle problems that help you notice different ways numeric and algebraic expressions can be equivalent, including how learners use the equals sign. You’ll meet two new module ideas: ‘Doing and undoing’ underpins some widely used methods of solving linear equations; ‘Productive lingering’ describes how teachers take time over small steps of algebraic reasoning. You’ll also undertake a project where you adapt a given task and work on it with your learner.
Unit 5: Invariance and change
You’ll focus on algebraic thinking as noticing change and, amidst this change, expressing properties or relationships that stay the same. You’ll tackle problems that require you to organise and represent change in one or more variables, particularly sequences problems. Additionally, you’ll create a presentation that identifies invariance and change in your algebraic reasoning.
Unit 6: Covariant relationships
This unit focuses on covariation: how two or more variables change in relation to one another. You’ll tackle problems involving algebraic expressions and graphs. You’ll also learn to use Cornerstone Maths and GeoGebra, two digital environments designed for education, to depict covariant relationships and reflect on the affordances of different representations.
Unit 7: Exploring functions and graphs
You’ll focus on functions, including the properties and contexts that give rise to linear, quadratic and exponential functions. Then, having now met all the module ideas, you’ll choose appropriate ones to identify algebraic thinking in your own mathematics and that of your learner. This forms the basis of your end-of-module assessment.
Unit 8: Progressing to geometry
This final unit connects algebra and geometry, supporting progression to Learning and doing geometry (ME321).
The full content list is on the Open mathematics and statistics website.
You’ll learn to:
This module is relevant to those who wish to pursue a career in education. It counts towards the mathematics degree content required to start secondary mathematics teacher training.
You’ll get help and support from an assigned tutor throughout your module.
They’ll help by:
Online tutorials run throughout the module. While they’re not compulsory, we strongly encourage you to participate. Where possible, we’ll make recordings available.
Course work includes:
You’ll have access to a module website, which includes:
Additionally, the website includes:
We also provide physical:
You can study this module on its own or use the credits you gain towards an Open University qualification.
ME322 is a compulsory module in our:
Learning and doing algebra (ME322) starts once a year – in October.
It will next start in October 2026.
We expect it to start for the last time in October 2029.
As a student of The Open University, you should be aware of the content of the academic regulations, which are available on our Student Policies and Regulations website.
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There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.
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